Discussion Questions 333

Q10.7 When an acrobat walks on a tightrope, she extends her armsstraight out from her sides. She does this to make it easier for herto catch herself if she should tip to one side or the other. Explainhow this works. [Hint: Think about Eq. (10.7).]Q10.8 When you turn on an electric motor, it takes longer to comeup to final speed if a grinding wheel is attached to the shaft. Why?Q10.9 Experienced cooks can tell whether an egg is raw or hard-boiled by rolling it down a slope (taking care to catch it at the bot-tom). How is this possible? What are they looking for?Q10.10 The work done by a force is the product of force and dis-tance. The torque due to a force is the product of force and dis-tance. Does this mean that torque and work are equivalent?Explain.Q10.11 A valued client brings a treasured ball to your engineeringfirm, wanting to know whether the ball is solid or hollow. He hastried tapping on it, but that has given insufficient information.Design a simple, inexpensive experiment that you could performquickly, without injuring the precious ball, to find out whether it issolid or hollow.Q10.12 You make two versions of the same object out of the samematerial having uniform density. For one version, all the dimen-sions are exactly twice as great as for the other one. If the sametorque acts on both versions, giving the smaller version angularacceleration , what will be the angular acceleration of the largerversion in terms of Q10.13 Two identical masses are attached to frictionless pulleysby very light strings wrapped around the rim of the pulley and arereleased from rest. Both pulleys have the same mass and samediameter, but one is solid and the other is a hoop. As the massesfall, in which case is the tension in the string greater, or is it thesame in both cases? Justify your answer.Q10.14 The force of gravity acts on the baton in Fig. 10.11, andforces produce torques that cause a body’s angular velocity tochange. Why, then, is the angular velocity of the baton in the figureconstant?Q10.15 A certain solid uniform ball reaches a maximum height when it rolls up a hill without slipping. What maximum height (interms of ) will it reach if you (a) double its diameter, (b) doubleits mass, (c) double both its diameter and mass, (d) double itsangular speed at the bottom of the hill?Q10.16 A wheel is rolling without slipping on a horizontal surface.In an inertial frame of reference in which the surface is at rest, isthere any point on the wheel that has a velocity that is purely verti-cal? Is there any point that has a horizontal velocity componentopposite to the velocity of the center of mass? Explain. Do youranswers change if the wheel is slipping as it rolls? Why or why not?Q10.17 Part of the kinetic energy of a moving automobile is in therotational motion of its wheels. When the brakes are applied hardon an icy street, the wheels “lock” and the car starts to slide. Whatbecomes of the rotational kinetic energy?Q10.18 A hoop, a uniform solid cylinder, a spherical shell, and auniform solid sphere are released from rest at the top of an incline.What is the order in which they arrive at the bottom of the incline?Does it matter whether or not the masses and radii of the objectsare all the same? Explain.Q10.19 A ball is rolling along at speed without slipping on a hor-izontal surface when it comes to a hill that rises at a constant angleabove the horizontal. In which case will it go higher up the hill: ifthe hill has enough friction to prevent slipping or if the hill is per-fectly smooth? Justify your answers in both cases in terms ofenergy conservation and in terms of Newton’s second law.

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Q10.20 You are standing at the center of a large horizontal turntablein a carnival funhouse. The turntable is set rotating on frictionlessbearings, and it rotates freely (that is, there is no motor driving theturntable). As you walk toward the edge of the turntable, what hap-pens to the combined angular momentum of you and the turntable?What happens to the rotation speed of the turntable? Explain youranswer.Q10.21 A certain uniform turntable of diameter has an angu-lar momentum If you want to redesign it so it retains the samemass but has twice as much angular momentum at the sameangular velocity as before, what should be its diameter in termsofQ10.22 A point particle travels in a straight line at constant speed,and the closest distance it comes to the origin of coordinates is adistance l. With respect to this origin, does the particle havenonzero angular momentum? As the particle moves along itsstraight-line path, does its angular momentum with respect to theorigin change?Q10.23 In Example 10.10 (Section 10.6) the angular speed changes, and this must mean that there is nonzero angular acceler-ation. But there is no torque about the rotation axis if the forces theprofessor applies to the weights are directly, radially inward. Then,by Eq. (10.7), must be zero. Explain what is wrong with thisreasoning that leads to this apparent contradiction.Q10.24 In Example 10.10 (Section 10.6) the rotational kineticenergy of the professor and dumbbells increases. But since thereare no external torques, no work is being done to change the rota-tional kinetic energy. Then, by Eq. (10.22), the kinetic energy mustremain the same! Explain what is wrong with this reasoning thatleads to this apparent contradiction. Where does the extra kineticenergy come from?Q10.25 As discussed in Section 10.6, the angular momentum of acircus acrobat is conserved as she tumbles through the air. Is herlinear momentum conserved? Why or why not?Q10.26 If you stop a spinning raw egg for the shortest possibleinstant and then release it, the egg will start spinning again. If youdo the same to a hard-boiled egg, it will remain stopped. Try it.Explain it.Q10.27 A helicopter has a large main rotor that rotates in a hori-zontal plane and provides lift. There is also a small rotor on the tailthat rotates in a vertical plane. What is the purpose of the tail rotor?(Hint: If there were no tail rotor, what would happen when thepilot changed the angular speed of the main rotor?) Some helicop-ters have no tail rotor, but instead have two large main rotors thatrotate in a horizontal plane. Why is it important that the two mainrotors rotate in opposite directions?Q10.28 In a common design for a gyroscope, the flywheel and fly-wheel axis are enclosed in a light, spherical frame with the fly-wheel at the center of the frame. The gyroscope is then balancedon top of a pivot so that the flywheel is directly above the pivot.Does the gyroscope precess if it is released while the flywheel isspinning? Explain.Q10.29 A gyroscope takes 3.8 s to precess 1.0 revolution about avertical axis. Two minutes later, it takes only 1.9 s to precess 1.0revolution. No one has touched the gyroscope. Explain.Q10.30 A gyroscope is precessing as in Fig. 10.32. What happensif you gently add some weight to the end of the flywheel axis far-thest from the pivot?Q10.31 A bullet spins on its axis as it emerges from a rifle. Explainhow this prevents the bullet from tumbling and keeps the stream-lined end pointed forward.

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